• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.1-28
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• 2004

We first apply a first order splitting to a semilinear reaction-diffusion equation and then discretize the resulting system by an $H^1$-Galerkin mixed finite element method in space. This semidiscrete method yields a system of differential algebraic equations (DAEs) of index one. A priori error estimates for semidiscrete scheme are derived for both differ-ential as well as algebraic components. For fully discretization, an implicit Runge-Kutta (IRK) methods is applied to the temporal direction and the error estimates are discussed for both components. Finally, we conclude the paper with a numerical example.

• Nuclear Engineering and Technology
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• v.14 no.4
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• pp.178-185
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• 1982

Albedo-type boundary condition is incorporated into the finite element formulation of the cubic Hermite polynomials for the two-dimensional solution of the two-group diffusion problem. Two modifications are introduced with respect to the conventional expression for the weak form of the group diffusion equation with the zero flux or zero current boundary condition and the cubic element functions over the boundary nodes. The finite element formulations obtained from those modifications are tested with the two-dimensional ZION problem. The numerical effectiveness of the modifications are examined.

• East Asian mathematical journal
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• v.33 no.5
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• pp.495-509
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• 2017

With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.

• The Journal of Advanced Prosthodontics
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• v.13 no.2
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• pp.79-88
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• 2021

Purpose. To assess peri-implant stress distribution using finite element analysis in implant supported fixed partial denture with occlusal schemes of cuspally loaded occlusion and implant protected occlusion. Materials and methods. A 3-D finite element model of mandible with D2 bone with partially edentulism with unilateral distal extension was made. Two Ti alloy identical implants with 4.2 mm diameter and 10 mm length were placed in the mandibular second premolar and the mandibular second molar region and prosthesis was given with the mandibular first molar pontic. Vertical load of 100 N and and oblique load of 70 N was applied on occlusal surface of prosthesis. Group 1 was cuspally loaded occlusion with total 8 contact points and Group 2 was implant protected occlusion with 3 contact points. Results. In Group 1 for vertical load, maximum stress was generated over implant having 14.3552 Mpa. While for oblique load, overall stress generated was 28.0732 Mpa. In Group 2 for vertical load, maximum stress was generated over crown and overall stress was 16.7682 Mpa. But for oblique load, crown stress and overall stress was maximum 22.7561 Mpa. When Group 1 is compared to Group 2, harmful oblique load caused maximum overall stress 28.0732 Mpa in Group 1. Conclusion. In Group 1, vertical load generated high implant stress, and oblique load generated high overall stresses, cortical stresses and crown stresses compared to vertical load. In Group 2, oblique load generated more overall stresses, cortical stresses, and crown stresses compared to vertical load. Implant protected occlusion generated lesser harmful oblique implant, crown, bone and overall stresses compared to cuspally loaded occlusion.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.345-353
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• 2002

Three noded plate and shell finite element and 3D beam element in conjunction with Lanczos method are used for studying the effect of boat tail angle on the free vibration characteristics of a typical payload fairing for three different cylinder diameters with height to diameter ratio 1.5. Configurations without boat tail structural member are also studied. One half of the one side fairing structure is considered for the analysis and symmetric boundary conditions are used.

• Structural Engineering and Mechanics
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• v.41 no.3
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• pp.395-406
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• 2012

Basic problem of pile foundation is three dimensional in nature. Three dimensional finite element formulation is employed for the analysis of pile groups. Pile, pile-cap and soil are modeled using 20 node element, whereas interface between pile or pile cap and soil is modeled using 16 node surface element. A parametric study is carried out to consider the effect of pile spacing, number of piles, arrangement of pile and soil modulus on the response of pile group. Results indicate that the response of pile group is dependent on these parameters.

• Biomaterials and Biomechanics in Bioengineering
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• v.3 no.2
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• pp.71-84
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• 2016

The finite element method is wide used in simulation in the biomechanical structures, but a lack of studies concerning finite element mesh quality in biomechanics is a reality. The present study intends to analyze the importance of the mesh quality in the finite element model results from humeral structure. A sensitivity analysis of finite element models (FEM) is presented for the humeral bone and cartilage structures. The geometry of bone and cartilage was acquired from CT scan and geometry reconstructed. The study includes 54 models from same bone geometry, with different mesh densities, constructed with tetrahedral linear elements. A finite element simulation representing the glenohumeral-joint reaction force applied on the humerus during $90^{\circ}$ abduction, with external load as the critical condition. Results from the finite element models suggest a mesh with 1.5 mm, 0.8 mm and 0.6 mm as suitable mesh sizes for cortical bone, trabecular bone and humeral cartilage, respectively. Relatively to the higher minimum principal strains are located at the proximal humerus diaphysis, and its highest value is found at the trabecular bone neck. The present study indicates the minimum mesh size in the finite element analyses in humeral structure. The cortical and trabecular bone, as well as cartilage, may not be correctly represented by meshes of the same size. The strain results presented the critical regions during the $90^{\circ}$ abduction.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.47-58
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• 2021

In this article, we completely determine the rings for which every element is a sum of a nilpotent and three tripotents that commute with one another. We discuss this property for some extensions of rings, including group rings.

• East Asian mathematical journal
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• v.19 no.1
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• pp.63-71
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• 2003

In his invited lecture presented during the First Conference of the Mathematical Society of the Republic of Moldova($Chi\c{s}in\v{a}u$, August 2001) W. A. Dudek posed several open problems on the role and properties of the skew element in the theory of n-ary groups. In this note we give the partial solutions of some of these problems.

• Design & Manufacturing
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• v.8 no.2
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• pp.46-49
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• 2014

Silicone is recently used for LED chip lense due to its good thermal stability and optical transmittance. In order to predict residual stress which causes optical briefringence and mechanical warpage of silicone, finite element analysis was conducted for curing process during silicone molding. For analysis of curing process, a dynamic cure kinetics model was derived based on the differential scanning calorimetry(DSC) test and applied to the material properties for finite element analysis. Finite element simulation result showed that the slow cure reduced abrupt reaction heat and it was predicted decrease of the residual stress.